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C7×Dic1105 #44525862

order30940
automorphism?
homologyAbelianization (H1) = C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×Dic1105

Splittings

derived, HallC5×C13×C17 ⋊ C4×C7
HallC5×C7×C13×C17 ⋊ C4
HallC7×C13×C17 ⋊ Dic5
HallC5×C7×C17 ⋊ Dic13
HallC5×C7×C13 ⋊ Dic17
HallC13×C17 ⋊ C7×Dic5
HallC7×C17 ⋊ Dic65
HallC7×C13 ⋊ Dic85
HallC5×C17 ⋊ C7×Dic13
HallC5×C13 ⋊ C7×Dic17
HallC5×C7 ⋊ Dic221
SylowC17 ⋊ C7×Dic65
SylowC13 ⋊ C7×Dic85
SylowC5 ⋊ C7×Dic221

Subgroups

subgroupG/H
center, hypercenterC2×C7D1105
commutator, hypocenterC5×C13×C17C4×C7
FrattiniC2C7×D1105
Fitting, socle, prime radicalC2×C5×C7×C13×C17C2
cosocleC2×C5×C13×C17C2×C7
LCSG ▷ C5×C13×C17
UCSC1 ◁ C2×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 30940

Conjugacy classes & character table

7756 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30940, 12);