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#49119131

order	36224
automorphism	?
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

Splittings

C₂₈₃ ⋊ #1290

Subgroups

	subgroup	G/H
center	C₂²	C₂₈₃⋊#95
commutator	C₂×C₄×C₂₈₃	C₄²
Frattini	C₂×C₄²	C₂×D₂₈₃
Fitting	C₂×C₄⋊C₈×C₂₈₃	C₂
socle	C₂²×C₂₈₃	#95
prime radical	C₂³×C₂₈₃	C₄⋊C₄
cosocle	C₂×C₄²×C₂₈₃	C₂²
hypercenter	C₂×C₄⋊C₈	D₂₈₃
hypocenter	C₂₈₃	#1290
LCS	G ▷ C₂×C₄×C₂₈₃ ▷ C₂×C₂₈₃ ▷ C₂₈₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

136 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 18112

Polycyclic presentation:

2^7,283|a^2=d,b^2=e,c^2=fg,d^2=f,e^2=fg,b^a=bc,c^a=cf,e^a=efg,h^a=h^282,d^b=dg

Conjugacy classes & character table

5672 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36224, 2380);