Finite Group Databasebeta

C4×#16863173 #30770658

order17152
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C42

Aliases

direct productC4×#16863173

Splittings

SylowC67 ⋊ C4×#347

Subgroups

subgroupG/H
centerC42C4×Dic67
commutatorC4×C67C43
FrattiniC22×C8C22×D67
FittingC4×M32×C67C2
socleC22×C67C2×#97
prime radicalC23×C67C2×M16
cosocleC22×C8×C67C23
hypercenterC4×M32D67
hypocenterC67C4×#347
LCSG ▷ C4×C67 ▷ C67
UCSC1 ◁ C42 ◁ C4×M32

418 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

2728 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 84395);