Finite Group Databasebeta

C2×C4×#10587495 #17031996

order4352
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C4×#10587495

Splittings

SylowC17 ⋊ C2×C4×#101

Subgroups

subgroupG/H
centerC22×C4#63227
commutatorC22×C17C22×C42
FrattiniC22×C4C23×D17
FittingC2×C4×M16×C17C2
socleC23×C17C2×C22⋊C4
prime radicalC24×C17C22×C4
cosocleC22×C4×C17C24
hypercenterC2×C4×M16D17
hypocenterC17C2×C4×#101
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×C4×M16

1538 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 167240);