Finite Group Databasebeta

C22⋊Q8×Dic191 #37575056

order24448
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC22⋊Q8×Dic191

Splittings

SylowC191 ⋊ C4×C22⋊Q8

Subgroups

subgroupG/H
center, FrattiniC23C23×D191
commutatorC22×C191C23×C4
FittingC2×C22⋊Q8×C191C2
socle, cosocleC23×C191C24
prime radicalC24×C191C23
hypercenterC2×C22⋊Q8D191
hypocenterC191C4×C22⋊Q8
LCSG ▷ C22×C191 ▷ C191
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

656 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12224

Conjugacy classes & character table

2716 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24448, 7046);