Finite Group Databasebeta

C4×#14583285 #25105133

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4×#14583285

Splittings

FittingC2×C4×SD16×C43 ⋊ C2
SylowC43 ⋊ C4×#496

Subgroups

subgroupG/H
centerC22×C4D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C4×SD16×C43C2
socleC23×C43C22×D4
prime radicalC2×#14583285C2
cosocleC22×C4×C43C24
hypercenterC2×C4×SD16D43
hypocenterC43C4×#496
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×SD16

1262 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1240 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 178104);