Finite Group Databasebeta

#2183×D67 #31009314

order17152
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C24

Aliases

direct product#2183×D67

Splittings

FittingC67×#2183 ⋊ C2
SylowC67 ⋊ C2×#2183

Subgroups

subgroupG/H
center, FrattiniC2×C8C23×D67
commutator, socleC22×C67C23×C8
FittingC67×#2183C2
prime radicalC22×D67C22×C8
cosocleC2×C8×C67C24
hypercenter#2183D67
hypocenterC67C2×#2183
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C2×C8 ◁ #2183

542 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

1960 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 323051);