Finite Group Databasebeta

#2117×D67 #31008530

order17152
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct product#2117×D67

Splittings

FittingC67×#2117 ⋊ C2
SylowC67 ⋊ C2×#2117

Subgroups

subgroupG/H
centerC8C2×D4×D67
commutatorC4×C67C23×C8
FrattiniC2×C8C23×D67
FittingC67×#2117C2
socleC2×C67C22×C22⋊C8
prime radicalC2×#41×D67C4
cosocleC2×C8×C67C24
hypercenter#2117D67
hypocenterC67C2×#2117
LCSG ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C8 ◁ C22×C8 ◁ #2117

1154 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2144

Conjugacy classes & character table

1540 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 322267);