Finite Group Databasebeta

C2×C4×#10587590 #17898350

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×C4×#10587590

Splittings

FittingC22×C4×C8×C17 ⋊ C2
SylowC17 ⋊ C2×C4×#135

Subgroups

subgroupG/H
centerC2×C42D68
commutatorC4×C17C24×C4
FrattiniC2×C4C24×D17
FittingC22×C4×C8×C17C2
socleC23×C17C22×D4
prime radicalC22×#10587590C2
cosocleC2×C4×C17C25
hypercenterC22×C4×C8D17
hypocenterC17C2×C4×#135
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C42 ◁ C22×C42 ◁ C22×C4×C8

2894 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

1136 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1033594);