Finite Group Databasebeta

C2×#28418271 #44472201

order29984
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×#28418271

Splittings

FittingC22×C4×C937 ⋊ C2
SylowC937 ⋊ C2×C22⋊C4

Subgroups

subgroupG/H
centerC23C2×D937
commutatorC2×C937C22×C4
FrattiniC22C22×D937
FittingC22×C4×C937C2
socleC23×C937C22
prime radicalC23×D937C2
cosocleC22×C937C23
hypercenterC22×C4D937
hypocenterC937C2×C22⋊C4
LCSG ▷ C2×C937 ▷ C937
UCSC1 ◁ C23 ◁ C22×C4

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14992

Conjugacy classes & character table

7508 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29984, 97);