Finite Group Databasebeta

C2×#22569250 #31720573

order17152
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#22569250

Splittings

SylowC67 ⋊ C2×#2975

Subgroups

subgroupG/H
centerC22×C4C23×D67
commutatorC22×C67C24×C4
FrattiniC2×C4C24×D67
FittingC22×C4×D4×C67C2
socleC23×C67C23×C4
prime radicalC23×D4×C67C4
cosocleC2×C4×C67C25
hypercenterC22×C4×D4D67
hypocenterC67C2×#2975
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C22×C4×D4

2586 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

2728 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1034310);