Finite Group Databasebeta

C4×#11762709 #16955508

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

Aliases

direct productC4×#11762709

Splittings

FittingC2×C4×C22⋊C4×C17 ⋊ C2
SylowC17 ⋊ C4×#390

Subgroups

subgroupG/H
centerC23×C4C22×D17
commutatorC22×C17C22×C42
FrattiniC24C23×D17
FittingC2×C4×C22⋊C4×C17C2
socle, cosocleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenterC2×C4×C22⋊C4D17
hypocenterC17C4×#390
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

2894 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 90752);