Finite Group Databasebeta

C2×#22561855 #31008558

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

Aliases

direct productC2×#22561855

Splittings

SylowC67 ⋊ C2×#2121

Subgroups

subgroupG/H
centerC22C2×#14523958
commutatorC23×C67C23×C4
FrattiniC2×D4C23×D67
Fitting, prime radicalC2×#534×C67C2
socleC22×C67C2×#99
cosocleC2×D4×C67C24
hypercenterC2×#534D67
hypocenterC67C2×#2121
LCSG ▷ C23×C67 ▷ C22×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ C24 ◁ C23×D4 ◁ C2×#534

1494 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2144

Conjugacy classes & character table

1498 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 322295);