Finite Group Databasebeta

C22⋊C4×Dic382 #37575355

order24448
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22⋊C4×Dic382

Splittings

SylowC191 ⋊ Q8×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D191
commutatorC22×C191C23×C4
FittingC4×C22⋊C4×C191C2
socle, cosocleC23×C191C24
prime radicalC24×C191C23
hypercenterC4×C22⋊C4D191
hypocenterC191Q8×C22⋊C4
LCSG ▷ C22×C191 ▷ C191
UCSC1 ◁ C23 ◁ C4×C22⋊C4

820 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12224

Conjugacy classes & character table

3850 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24448, 7345);