Finite Group Databasebeta

C2×#14544714 #17969601

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#14544714

Splittings

FittingC2×C4×C8×C17 ⋊ C4
SylowC17 ⋊ C2×#1841

Subgroups

subgroupG/H
centerC2×C4#10587677
commutatorC2×C4×C17C23×C4
FrattiniC2×C4C23×#595
FittingC2×C4×C8×C17C4
socleC22×C17#383
prime radicalC23×D17#41
cosocleC2×C4×D17C24
hypercenterC2×C4×C8#595
hypocenterC17C2×#1841
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×C4×C8

730 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

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, 1104845);