Finite Group Databasebeta

C2×C4×#13063284 #25254782

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

Aliases

direct productC2×C4×#13063284

Splittings

SylowC43 ⋊ C2×C4×#117

Subgroups

subgroupG/H
centerC22×C42C2×D43
commutatorC2×C43C23×C42
FrattiniC23C24×D43
FittingC23×C42×C43C2
socleC24×C43C24
prime radicalC25×C43C23
cosocleC23×C43C25
hypercenterC23×C42D43
hypocenterC43C2×C4×#117
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C42 ◁ C23×C42

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, 327753);