Finite Group Databasebeta

C22×#16863149 #30824800

order17152
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC22×#16863149

Splittings

SylowC67 ⋊ C22×#335

Subgroups

subgroupG/H
centerC23×C4D268
commutatorC4×C67C23×C8
FrattiniC42C23×D67
FittingC22×C4×C8×C67C2
socle, prime radicalC24×C67C4⋊C4
cosocleC42×C67C24
hypercenterC22×C4×C8D67
hypocenterC67C22×#335
LCSG ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23×C4 ◁ C22×C42 ◁ C22×C4×C8

942 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17152

Conjugacy classes & character table

4336 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 138537);