Finite Group Databasebeta

C2×2−1+4×Dic17 #17940934

order4352
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC2×2−1+4×Dic17

Splittings

SylowC17 ⋊ C2×C4×2−1+4

Subgroups

subgroupG/H
centerC23C24×D17
commutatorC2×C17C25×C4
FrattiniC22C25×D17
Fitting, prime radicalC22×C17×2−1+4C2
socleC23×C17C25
cosocleC22×C17C26
hypercenterC22×2−1+4D17
hypocenterC17C2×C4×2−1+4
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×2−1+4

11210 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1076178);