Finite Group Databasebeta

C2×#14526614 #16923739

order4352
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct productC2×#14526614

Splittings

SylowC17 ⋊ C2×#1275

Subgroups

subgroupG/H
centerC22×C4C4×Dic17
commutatorC4×C17C2×C4×C8
FrattiniC2×C42C22×D17
FittingC2×C17×#431C2
socleC23×C17#95
prime radicalC24×C17C4⋊C4
cosocleC2×C42×C17C23
hypercenterC2×#431D17
hypocenterC17C2×#1275
LCSG ▷ C4×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×#431

678 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, 58983);