Finite Group Databasebeta

C2×C4×#13063282 #25254783

order11008
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C27×C42

Aliases

direct productC2×C4×#13063282

Splittings

FittingC2×C43×C43 ⋊ C2
SylowC43 ⋊ C2×C4×#117

Subgroups

subgroupG/H
centerC22×C42C2×D43
commutatorC2×C43C23×C42
FrattiniC23C24×D43
FittingC2×C43×C43C2
socleC24×C43C24
prime radicalC24×D43C23
cosocleC23×C43C25
hypercenterC2×C43D43
hypocenterC43C2×C4×#117
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C42 ◁ C2×C43

4462 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2848 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 327754);