Finite Group Databasebeta

C2×#19132432 #24986089

order11008
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×#19132432

Splittings

SylowC43 ⋊ C2×#1278

Subgroups

subgroupG/H
centerC2×C42D172
commutatorC4×C43C2×C4×C8
FrattiniC2×C42C22×D43
FittingC22×C4×C8×C43C2
socleC23×C43#95
prime radicalC24×C43C4⋊C4
cosocleC2×C42×C43C23
hypercenterC22×C4×C8D43
hypocenterC43C2×#1278
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C42 ◁ C22×C42 ◁ C22×C4×C8

782 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 59060);