Finite Group Databasebeta

C4×#16863872 #31014080

order17152
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC4×#16863872

Splittings

FittingC42×Q8×C67 ⋊ C2
SylowC67 ⋊ C4×#519

Subgroups

subgroupG/H
centerC22×C4C23×D67
commutatorC2×C67C23×C42
FrattiniC23C24×D67
FittingC42×Q8×C67C2
socle, cosocleC23×C67C25
prime radicalC23×D67C24
hypercenterC42×Q8D67
hypocenterC67C4×#519
LCSG ▷ C2×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C42×Q8

3402 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

2776 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 327817);