Finite Group Databasebeta

C4×#16864162 #31719244

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

Aliases

direct productC4×#16864162

Splittings

FittingC2×C4×M16×C67 ⋊ C2
SylowC67 ⋊ C4×#568

Subgroups

subgroupG/H
centerC42C23×D67
commutatorC2×C67C23×C42
FrattiniC2×C4C24×D67
FittingC2×C4×M16×C67C2
socleC22×C67C24×C4
prime radicalC22×#11761628C22
cosocleC2×C4×C67C25
hypercenterC2×C4×M16D67
hypocenterC67C4×#568
LCSG ▷ C2×C67 ▷ C67
UCSC1 ◁ C42 ◁ C2×C4×M16

3250 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

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, 1032981);