Finite Group Databasebeta

C22×Dic746 #26045832

order11936
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC22×Dic746

Splittings

SylowC373 ⋊ C22×Q8

Subgroups

subgroupG/H
centerC23C2×D373
commutator, cosocleC2×C373C24
FrattiniC2C23×D373
FittingC22×C4×C373C2
socle, prime radicalC23×C373C22
hypercenterC22×C4D373
hypocenterC373C22×Q8
LCSG ▷ C2×C373 ▷ C373
UCSC1 ◁ C23 ◁ C22×C4

156 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#37559326, #37559327, #37559328, …
maximal normal subgroup of#37559326, #37559327, #37559328, …
maximal quotient ofC22×#20238589, C22×C4⋊Dic373, C2×C4×Dic746, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11936, 186);