Finite Group Databasebeta

C4×#21418744 #44470507

order29888
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#21418744

Splittings

FittingC4×Q8×C467 ⋊ C2
SylowC467 ⋊ C4×#41

Subgroups

subgroupG/H
centerC2×C4C22×D467
commutatorC2×C467C23×C4
FrattiniC22C23×D467
FittingC4×Q8×C467C2
socle, cosocleC22×C467C24
prime radicalC2×#21418744C2
hypercenterC4×Q8D467
hypocenterC467C4×#41
LCSG ▷ C2×C467 ▷ C467
UCSC1 ◁ C2×C4 ◁ C4×Q8

310 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14944

Conjugacy classes & character table

4700 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29888, 1019);