Finite Group Databasebeta

C2×#14543647 #17950951

order4352
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C25

Aliases

direct productC2×#14543647

Splittings

FittingC23×C8×C17 ⋊ C4
SylowC17 ⋊ C2×#1289

Subgroups

subgroupG/H
centerC23(C2×#595)⋊C4
commutatorC2×C4×C17C2×C42
FrattiniC22×C4C22×#595
FittingC23×C8×C17C4
socleC23×C17#95
prime radicalC24×D17D4
cosocleC22×C4×D17C23
hypercenterC23×C8#595
hypocenterC17C2×#1289
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8

1130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1086195);