D₇×C₅⋊D₉₅ #27210909

order	13300
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂×C₅

Aliases

direct product	D₇×C₅⋊D₉₅
unambiguous semidirect product	(C₅×D₇)⋊D₉₅
unambiguous semidirect product	(D₇×C₁₉)⋊(C₅⋊D₅)

Splittings

Fitting, socle, derived, Hall	C₅²×C₇×C₁₉ ⋊ C₂²
Hall	C₅²×C₁₉ ⋊ C₂×D₇
Hall	C₅²×C₇ ⋊ C₂×D₁₉
Hall	C₇×C₁₉ ⋊ C₂×C₅⋊D₅
Sylow	C₅² ⋊ D₇×D₁₉
Sylow	C₁₉ ⋊ D₇×C₅⋊D₅
Sylow	C₇ ⋊ C₂×C₅⋊D₉₅

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅²×C₇×C₁₉	C₂²
LCS	G ▷ C₅²×C₇×C₁₉
UCS	C₁

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 36
transitive degree	μ_t(G) = 3325

A minimal faithful permutation representation — 3 generators on 36 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21,23,25,26,24,22)(28,29)(30,31)(33,34)(35,36);(1,2,4,6,8,10,12,14,16,18,19,17,15,13,11,9,7,5,3)(21,22)(23,24)(25,26)(32,33,35,36,34);(27,28,30,31,29)

Conjugacy classes & character table

1195 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13300, 67);

D7×C5⋊D95 #27210909