Finite Group Databasebeta

C22×#16863203 #31008754

order17152
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22×#16863203

Splittings

SylowC67 ⋊ C22×#359

Subgroups

subgroupG/H
centerC22×C4#11761613
commutatorC8×C67C23×C4
FrattiniC2×C8C23×D67
Fitting, prime radicalC22×#135×C67C2
socleC23×C67#102
cosocleC2×C8×C67C24
hypercenterC22×#135D67
hypocenterC67C22×#359
LCSG ▷ C8×C67 ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C23×C8 ◁ C22×#135

1174 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

1936 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 322491);