Finite Group Databasebeta

#102×C22⋊D67 #30871233

order17152
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct product#102×C22⋊D67

Splittings

FittingC22×#102×C67 ⋊ C2
SylowC67 ⋊ D4×#102

Subgroups

subgroupG/H
centerC23C2×D4×D67
commutatorC2×C4×C67C23×C4
FrattiniC22×C4C23×D67
FittingC22×#102×C67C2
socleC23×C67C22×D4
prime radicalC2×D4×C22⋊D67C2
cosocleC22×C4×C67C24
hypercenterC22×#102D67
hypocenterC67D4×#102
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#102

2014 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

1918 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 184970);