Finite Group Databasebeta

← Prev (#25094243) Next (#25094245) →

C2×C4×#13063239 #25094244

order11008
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×C4×#13063239

Splittings

FittingC2×C4×C22⋊C4×C43 ⋊ C2
SylowC43 ⋊ C2×C4×#99

Subgroups

subgroupG/H
centerC22×C4(C2×D43)⋊C4
commutatorC22×C43C22×C42
FrattiniC24C23×D43
FittingC2×C4×C22⋊C4×C43C2
socleC23×C43C2×C22⋊C4
prime radicalC23×C22⋊D43C22
cosocleC24×C43C24
hypercenterC2×C4×C22⋊C4D43
hypocenterC43C2×C4×#99
LCSG ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C2×C4×C22⋊C4

2242 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1768 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 167215);