Finite Group Databasebeta

C2×#14524062 #16864175

order4288
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#14524062

Splittings

FittingC2×D8×C67 ⋊ C2
SylowC67 ⋊ C2×#135

Subgroups

subgroupG/H
centerC22D4×D67
commutator, cosocleC4×C67C24
FrattiniC4C23×D67
FittingC2×D8×C67C2
socleC22×C67C2×D4
hypercenterC2×D8D67
hypocenterC67C2×#135
LCSG ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

266 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2144

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4288, 1328);