Finite Group Databasebeta

C22⋊Q8×Dic227 #44402270

order29056
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC22⋊Q8×Dic227

Splittings

SylowC227 ⋊ C4×C22⋊Q8

Subgroups

subgroupG/H
center, FrattiniC23C23×D227
commutatorC22×C227C23×C4
FittingC2×C22⋊Q8×C227C2
socle, cosocleC23×C227C24
prime radicalC24×C227C23
hypercenterC2×C22⋊Q8D227
hypocenterC227C4×C22⋊Q8
LCSG ▷ C22×C227 ▷ C227
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

656 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14528

Conjugacy classes & character table

3220 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29056, 7046);