D₁₃₃₉₅ #40999545

order	26790
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₃₃₉₅
unambiguous semidirect product	C₃⋊D₄₄₆₅
unambiguous semidirect product	C₅⋊D₂₆₇₉
unambiguous semidirect product	C₁₉⋊D₇₀₅
unambiguous semidirect product	C₄₇⋊D₂₈₅

Splittings

Fitting, socle, derived, Hall	C₃×C₅×C₁₉×C₄₇ ⋊ C₂
Hall	C₅×C₁₉×C₄₇ ⋊ D₃
Hall	C₃×C₁₉×C₄₇ ⋊ D₅
Hall	C₁₉×C₄₇ ⋊ D₁₅
Hall	C₃×C₅×C₄₇ ⋊ D₁₉
Hall	C₃×C₅×C₁₉ ⋊ D₄₇
Hall	C₅×C₄₇ ⋊ D₅₇
Hall	C₃×C₄₇ ⋊ D₉₅
Hall	C₅×C₁₉ ⋊ D₁₄₁
Hall	C₃×C₁₉ ⋊ D₂₃₅
Sylow	C₄₇ ⋊ D₂₈₅
Sylow	C₁₉ ⋊ D₇₀₅
Hall	C₃×C₅ ⋊ D₈₉₃
Sylow	C₅ ⋊ D₂₆₇₉
Sylow	C₃ ⋊ D₄₄₆₅

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅×C₁₉×C₄₇	C₂
LCS	G ▷ C₃×C₅×C₁₉×C₄₇
UCS	C₁

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 74
transitive degree	μ_t(G) = 13395

A minimal faithful permutation representation — 2 generators on 74 points:

(1,2,3)(4,5,6,7,8)(9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27)(28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74);(2,3)(5,8)(6,7)(10,27)(11,26)(12,25)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)(29,74)(30,73)(31,72)(32,71)(33,70)(34,69)(35,68)(36,67)(37,66)(38,65)(39,64)(40,63)(41,62)(42,61)(43,60)(44,59)(45,58)(46,57)(47,56)(48,55)(49,54)(50,53)(51,52)

Polycyclic presentation:

2,3,5,19,47|b^a=b^2,c^a=c^4,d^a=d^18,e^a=e^46

Conjugacy classes & character table

6699 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×D₁₃₃₉₅
maximal normal subgroup of	C₂×D₁₃₃₉₅
maximal quotient of	Dic₁₃₃₉₅, C₂×D₁₃₃₉₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26790, 17);

D13395 #40999545