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C3×C22⋊Dic35 #13132304

order1680
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22

Aliases

direct productC3×C22⋊Dic35

Splittings

HallC3×C5×C7 ⋊ C22⋊C4
HallC5×C7 ⋊ C3×C22⋊C4
HallC3×C7 ⋊ C22⋊Dic5
HallC3×C5 ⋊ C22⋊Dic7
SylowC7 ⋊ C3×C22⋊Dic5
SylowC5 ⋊ C3×C22⋊Dic7

Subgroups

subgroupG/H
centerC22×C3C2×D35
commutatorC2×C5×C7C2×C3×C4
FrattiniC22C2×C3×D35
Fitting, prime radicalC23×C3×C5×C7C2
socleC22×C3×C5×C7C22
cosocleC22×C5×C7C22×C3
hypercenterC23×C3D35
hypocenterC5×C7C3×C22⋊C4
LCSG ▷ C2×C5×C7 ▷ C5×C7
UCSC1 ◁ C22×C3 ◁ C23×C3

136 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 840

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1680, 324);