Finite Group Databasebeta

#2230×D67 #31010557

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

Aliases

direct product#2230×D67

Splittings

FittingC67×#2230 ⋊ C2
SylowC67 ⋊ C2×#2230

Subgroups

subgroupG/H
centerC2#476×D67
commutator, cosocleC2×C8×C67C24
FrattiniC2×C8C23×D67
FittingC67×#2230C2
socleC2×C67C2×#476
prime radical#135×D67C22
hypercenter#2230D67
hypocenterC67C2×#2230
LCSG ▷ C2×C8×C67 ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2230

558 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1072

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 324294);