Finite Group Databasebeta

C2×C4×#13063296 #25255017

order11008
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×C4×#13063296

Splittings

FittingC22×C4×D4×C43 ⋊ C2
SylowC43 ⋊ C2×C4×#121

Subgroups

subgroupG/H
centerC23×C4C22×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC22×C4×D4×C43C2
socleC24×C43C24
prime radicalC22×#13063296C2
cosocleC23×C43C25
hypercenterC22×C4×D4D43
hypocenterC43C2×C4×#121
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23×C4 ◁ C22×C4×D4

5022 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1792 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 327988);