Finite Group Databasebeta

C2×#28417864 #44469986

order29888
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23

Aliases

direct productC2×#28417864

Splittings

SylowC467 ⋊ C2×#97

Subgroups

subgroupG/H
centerC22×C4C2×D467
commutatorC2×C467C2×C42
FrattiniC2×C4C22×D467
FittingC2×C42×C467C2
socle, prime radicalC23×C467C2×C4
cosocleC2×C4×C467C23
hypercenterC2×C42D467
hypocenterC467C2×#97
LCSG ▷ C2×C467 ▷ C467
UCSC1 ◁ C22×C4 ◁ C2×C42

146 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, 498);