Finite Group Databasebeta

C2×C4×#3828 #11899952

order1152
isoclinismisoclinic class of #634
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29×C3

Aliases

direct productC2×C4×#3828

Splittings

FittingC22×C32×C42 ⋊ C2
SylowC32 ⋊ C2×C4×#41

Subgroups

subgroupG/H
centerC2×C42C2×C3⋊D3
commutatorC2×C32C24×C4
FrattiniC22C24×C3⋊D3
FittingC22×C32×C42C2
socleC23×C32C24
prime radicalC22×#3828C2
cosocleC22×C32C25
hypercenterC22×C42C3⋊D3
hypocenterC32C2×C4×#41
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C42 ◁ C22×C42

5184 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 576

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 133963);