C₂₅×C₃⋊D₈₇ #27189386

order	13050
automorphism	?
homology	Abelianization (H₁) = C₂×C₂₅ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₂₅×C₃⋊D₈₇
unambiguous semidirect product	C₃⋊(C₂₅×D₈₇)
unambiguous semidirect product	C₂₉⋊(C₃⋊D₃×C₂₅)

Splittings

Fitting, Hall	C₃²×C₂₅×C₂₉ ⋊ C₂
derived, Hall	C₃²×C₂₉ ⋊ C₂×C₂₅
Hall	C₂₅×C₂₉ ⋊ C₃⋊D₃
Hall	C₃²×C₂₅ ⋊ D₂₉
Sylow	C₂₉ ⋊ C₃⋊D₃×C₂₅
Sylow	C₃² ⋊ C₂₅×D₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂₅	C₃⋊D₈₇
commutator, hypocenter	C₃²×C₂₉	C₂×C₂₅
Frattini	C₅	C₅×C₃⋊D₈₇
Fitting	C₃²×C₂₅×C₂₉	C₂
socle, cosocle	C₃²×C₅×C₂₉	C₂×C₅
prime radical	C₅×C₃⋊D₈₇	C₅
LCS	G ▷ C₃²×C₂₉
UCS	C₁ ◁ C₂₅

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 60
transitive degree	μ_t(G) = 6525

A minimal faithful permutation representation — 3 generators on 60 points:

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

Conjugacy classes & character table

3300 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃⋊D₃×C₂₅×D₂₉, D₂₅×C₃⋊D₈₇, D₇₂₅⋊(C₃⋊D₃), …
maximal normal subgroup of	C₃⋊D₃×C₂₅×D₂₉, D₂₅×C₃⋊D₈₇, D₇₂₅⋊(C₃⋊D₃), …
maximal quotient of	C₂₅×C₃⋊Dic₈₇, C₂×C₂₅×C₃⋊D₈₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13050, 18);

C25×C3⋊D87 #27189386