Finite Group Databasebeta

C4×#16863130 #30746705

order17152
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productC4×#16863130

Splittings

SylowC67 ⋊ C4×#327

Subgroups

subgroupG/H
centerC22×C4C22⋊Dic67
commutatorC2×C4×C67C2×C42
FrattiniC23×C4C22×D67
FittingC4×#121×C67C2
socleC23×C67C2×C22⋊C4
prime radicalC2×#121×C67C22
cosocleC23×C4×C67C23
hypercenterC4×#121D67
hypocenterC67C4×#327
LCSG ▷ C2×C4×C67 ▷ C22×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×#121

816 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

1924 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 60442);