C₅×D₁₃×D₉₁ #37556854

order	23660
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₅×D₁₃×D₉₁
unambiguous semidirect product	(C₇×D₁₃)⋊(C₅×D₁₃)
unambiguous semidirect product	(C₁₃×D₁₃)⋊(C₅×D₇)

Splittings

Fitting, socle, Hall	C₅×C₇×C₁₃² ⋊ C₂²
derived, Hall	C₇×C₁₃² ⋊ C₂²×C₅
Hall	C₅×C₁₃² ⋊ C₂×D₇
Sylow	C₁₃² ⋊ C₂×C₅×D₇
Hall	C₅×C₇ ⋊ D₁₃²
Sylow	C₇ ⋊ C₅×D₁₃²

Subgroups

	subgroup	G/H
center, hypercenter	C₅	D₁₃×D₉₁
commutator, cosocle, hypocenter	C₇×C₁₃²	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₁₃²	C₂²
LCS	G ▷ C₇×C₁₃²
UCS	C₁ ◁ C₅

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 38
transitive degree	μ_t(G) = 910

A minimal faithful permutation representation — 2 generators on 38 points:

(2,3)(4,5)(6,7)(8,9,11,13,15,17,19,20,18,16,14,12,10)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35,36,37,38);(1,2,4,6,7,5,3)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22,24,26,28,30,32,33,31,29,27,25,23)

Conjugacy classes & character table

1880 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23660, 84);

C5×D13×D91 #37556854