Finite Group Databasebeta

C2×#20238587 #26045743

order11936
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×#20238587

Splittings

FittingC22×C4×C373 ⋊ C2
SylowC373 ⋊ C2×C22⋊C4

Subgroups

subgroupG/H
centerC23C2×D373
commutatorC2×C373C22×C4
FrattiniC22C22×D373
FittingC22×C4×C373C2
socleC23×C373C22
prime radicalC23×D373C2
cosocleC22×C373C23
hypercenterC22×C4D373
hypocenterC373C2×C22⋊C4
LCSG ▷ C2×C373 ▷ C373
UCSC1 ◁ C23 ◁ C22×C4

132 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2996 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#37559145, #37559269, C4×#20238587, …
maximal normal subgroup of#37559145, #37559269, C4×#20238587, …
maximal quotient ofC2×#26045699, C4×#20238587, #37559277, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11936, 97);