C₂₉₉₉⋊C₈ #37561985

order	23992
automorphism	?
homology	Abelianization (H₁) = C₈ · Schur multiplier (H₂) = C₁

Aliases

C₂₉₉₉⋊C₈

C₂₉₉₉ ⋊ C₈

	subgroup	G/H
center, Frattini, hypercenter	C₄	D₂₉₉₉
commutator, hypocenter	C₂₉₉₉	C₈
Fitting, cosocle	C₄×C₂₉₉₉	C₂
socle, prime radical	C₂×C₂₉₉₉	C₄
LCS	G ▷ C₂₉₉₉
UCS	C₁ ◁ C₄

8 conjugacy classes of subgroups.

μ_t(G) = 23992

Polycyclic presentation:

2^3,2999|a^2=b,b^2=c,d^a=d^2998

6004 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23992, 6);