Finite Group Databasebeta

C2×#28417898 #44470462

order29888
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#28417898

Splittings

FittingC2×C16×C467 ⋊ C2
SylowC467 ⋊ C2×SD32

Subgroups

subgroupG/H
centerC22D3736
commutator, cosocleC8×C467C23
FrattiniC8C22×D467
FittingC2×C16×C467C2
socleC22×C467D8
prime radicalC2×D3736C2
hypercenterC2×C16D467
hypocenterC467C2×SD32
LCSG ▷ C8×C467 ▷ C4×C467 ▷ C2×C467 ▷ C467
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14944

Conjugacy classes & character table

7478 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29888, 974);