Finite Group Databasebeta

C2×#19138961 #25265703

order11008
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×#19138961

Splittings

FittingC22×C4⋊Q8×C43 ⋊ C2
SylowC43 ⋊ C2×#2491

Subgroups

subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC22×C4⋊Q8×C43C2
socleC24×C43C24
prime radicalC22×#13063300C2
hypercenterC22×C4⋊Q8D43
hypocenterC43C2×#2491
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×C4⋊Q8

3678 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1252 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 338674);