Finite Group Databasebeta

C22×Dic367⋊C4 #37554636

order23488
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22×Dic367⋊C4

Splittings

SylowC367 ⋊ C22×C4⋊C4

Subgroups

subgroupG/H
centerC24C2×D367
commutatorC2×C367C23×C4
FrattiniC22C23×D367
FittingC23×C4×C367C2
socle, prime radicalC24×C367C22
cosocleC22×C367C24
hypercenterC23×C4D367
hypocenterC367C22×C4⋊C4
LCSG ▷ C2×C367 ▷ C367
UCSC1 ◁ C24 ◁ C23×C4

418 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 23488

Conjugacy classes & character table

5896 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23488, 999);