Finite Group Databasebeta

#322×Dic67 #30745178

order17152
automorphism?
homologyAbelianization (H1) = C42×C8 · Schur multiplier (H2) = C43

Aliases

direct product#322×Dic67

Splittings

SylowC67 ⋊ C4×#322

Subgroups

subgroupG/H
center, FrattiniC2×C42C22×D67
commutatorC2×C67C42×C8
FittingC2×#322×C67C2
socle, prime radicalC23×C67C2×C42
cosocleC2×C42×C67C23
hypercenterC2×#322D67
hypocenterC67C4×#322
LCSG ▷ C2×C67 ▷ C67
UCSC1 ◁ C2×C42 ◁ C2×#322

654 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17152

Conjugacy classes & character table

2800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 58915);