Finite Group Databasebeta

C4×#16863455 #30853976

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

Aliases

direct productC4×#16863455

Splittings

FittingC42×C8×C67 ⋊ C2
SylowC67 ⋊ C4×#433

Subgroups

subgroupG/H
centerC2×C42C22×D67
commutatorC22×C67C22×C42
FrattiniC22×C4C23×D67
FittingC42×C8×C67C2
socleC23×C67C23×C4
prime radicalC23×D67C22×C4
cosocleC22×C4×C67C24
hypercenterC42×C8D67
hypocenterC67C4×#433
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C2×C42 ◁ C42×C8

970 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

4336 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 167713);