Finite Group Databasebeta

C4×#16863456 #30853977

order17152
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C22×C42

Aliases

direct productC4×#16863456

Splittings

FittingC4×C4⋊C8×C67 ⋊ C2
SylowC67 ⋊ C4×#433

Subgroups

subgroupG/H
centerC2×C42C22×D67
commutatorC22×C67C22×C42
FrattiniC22×C4C23×D67
FittingC4×C4⋊C8×C67C2
socleC23×C67C23×C4
prime radicalC23×D67C22×C4
cosocleC22×C4×C67C24
hypercenterC4×C4⋊C8D67
hypocenterC67C4×#433
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C2×C42 ◁ C4×C4⋊C8

970 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

2752 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 167714);