Finite Group Databasebeta

#101×C22⋊D67 #30871198

order17152
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct product#101×C22⋊D67

Splittings

FittingC22×#101×C67 ⋊ C2
SylowC67 ⋊ D4×#101

Subgroups

subgroupG/H
centerC22C2×C22⋊C4×D67
commutatorC23×C67C23×C4
FrattiniC22×C4C23×D67
FittingC22×#101×C67C2
socleC22×C67C22×C22⋊C4
prime radicalC22×C22⋊D67C2×C4
cosocleC22×C4×C67C24
hypercenterC22×#101D67
hypocenterC67D4×#101
LCSG ▷ C23×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#101

1378 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

1507 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 184935);