Finite Group Databasebeta

C2×(C2×D1187)⋊C4 #49184205

order37984
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×(C2×D1187)⋊C4

Splittings

FittingC22×C4×C1187 ⋊ C2
SylowC1187 ⋊ C2×C22⋊C4

Subgroups

subgroupG/H
centerC23C2×D1187
commutatorC2×C1187C22×C4
FrattiniC22C22×D1187
FittingC22×C4×C1187C2
socleC23×C1187C22
prime radicalC23×D1187C2
cosocleC22×C1187C23
hypercenterC22×C4D1187
hypocenterC1187C2×C22⋊C4
LCSG ▷ C2×C1187 ▷ C1187
UCSC1 ◁ C23 ◁ C22×C4

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18992

Conjugacy classes & character table

9508 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37984, 97);