Finite Group Databasebeta

C22×C4⋊Dic467 #44470488

order29888
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22×C4⋊Dic467

Splittings

SylowC467 ⋊ C22×C4⋊C4

Subgroups

subgroupG/H
centerC24C2×D467
commutatorC2×C467C23×C4
FrattiniC22C23×D467
FittingC23×C4×C467C2
socle, prime radicalC24×C467C22
cosocleC22×C467C24
hypercenterC23×C4D467
hypocenterC467C22×C4⋊C4
LCSG ▷ C2×C467 ▷ C467
UCSC1 ◁ C24 ◁ C23×C4

418 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 29888

Conjugacy classes & character table

7496 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29888, 1000);