Finite Group Databasebeta

C2×#41×C43⋊C8 #25961031

order11008
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C29

Aliases

direct productC2×#41×C43⋊C8

Splittings

SylowC43 ⋊ C2×C8×#41

Subgroups

subgroupG/H
centerC2×C42C22×D43
commutatorC2×C43C24×C8
FrattiniC2×C4C24×D43
FittingC2×C4×#41×C43C2
socleC23×C43C23×C4
prime radicalC22×#41×C43C4
cosocleC2×C4×C43C25
hypercenterC2×C4×#41D43
hypocenterC43C2×C8×#41
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C42 ◁ C2×C4×#41

2566 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1840 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1034002);