Finite Group Databasebeta

C2×#28417910 #44470491

order29888
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#28417910

Splittings

FittingC2×C42×C467 ⋊ C2
SylowC467 ⋊ C2×#117

Subgroups

subgroupG/H
centerC22×C4C2×D467
commutatorC2×C467C23×C4
FrattiniC22C23×D467
FittingC2×C42×C467C2
socleC23×C467C23
prime radicalC23×D467C22
cosocleC22×C467C24
hypercenterC2×C42D467
hypocenterC467C2×#117
LCSG ▷ C2×C467 ▷ C467
UCSC1 ◁ C22×C4 ◁ C2×C42

330 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14944

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, 1003);