#29503137

order	15162
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

No aliases for this group.

Splittings

Fitting, socle, derived, Hall	C₇×C₁₉² ⋊ C₂×C₃
Hall	C₇×#11762245 ⋊ C₂
Hall	C₇⋊(C₁₉⋊D₁₉) ⋊ C₃
Hall	#11762245 ⋊ D₇
Sylow	C₁₉² ⋊ C₃×D₇
Sylow	C₇ ⋊ #14524206

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₁₉²	C₂×C₃
LCS	G ▷ C₇×C₁₉²
UCS	C₁

176 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 45
transitive degree	μ_t(G) = 2527

A minimal faithful permutation representation — 3 generators on 45 points:

(2,3)(4,5)(6,7)(9,13,14,10,11,15)(12,21,18,16,17,23)(19,24,26,25,22,20)(28,32,33,29,30,34)(31,40,37,35,36,42)(38,43,45,44,41,39);(1,2,4,6,7,5,3)(27,28,31,37,43,40,44,30,34,39,45,33,32,38,36,41,42,35,29);(8,9,12,18,24,21,25,11,15,20,26,14,13,19,17,22,23,16,10)

Polycyclic presentation:

2,3,7,19^2|c^a=c^6,d^a=d^18,e^a=e^18,d^b=d^7,e^b=e^7

Conjugacy classes & character table

435 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₇×#14524206, #14524208⋊D₇, C₂×#29503137
maximal normal subgroup of	D₇×#14524206, #14524208⋊D₇, C₂×#29503137
maximal quotient of	#44476529, C₂×#29503137

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15162, 72);