Finite Group Databasebeta

C4×#11763225 #17186966

order4352
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4×#11763225

Splittings

FittingC2×C4×C16×C17 ⋊ C2
SylowC17 ⋊ C4×#504

Subgroups

subgroupG/H
centerC4×C16C2×D17
commutatorC2×C17C22×C4×C8
FrattiniC2×C8C23×D17
FittingC2×C4×C16×C17C2
socleC22×C17C23×C8
prime radicalC2×#63252C2×C4
cosocleC2×C8×C17C24
hypercenterC2×C4×C16D17
hypocenterC17C4×#504
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C4×C16 ◁ C2×C4×C16

834 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

1184 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 322210);