Finite Group Databasebeta

C2×#22561098 #30859773

order17152
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#22561098

Splittings

SylowC67 ⋊ C2×#1974

Subgroups

subgroupG/H
centerC22×C4D4×D67
commutatorC2×C4×C67C23×C4
FrattiniC22×C4C23×D67
Fitting, prime radicalC22×#135×C67C2
socleC23×C67C4×D4
cosocleC22×C4×C67C24
hypercenterC22×#135D67
hypocenterC67C2×#1974
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×#135

1558 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

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, 173510);