Finite Group Databasebeta

C2×#22574714 #31763274

order17152
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C213

Aliases

direct productC2×#22574714

Splittings

SylowC67 ⋊ C2×#3557

Subgroups

subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
Fitting, prime radicalC2×#540×C67C2
socleC23×C67C25
hypercenterC2×#540D67
hypocenterC67C2×#3557
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#540

6554 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

1528 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1077011);