Finite Group Databasebeta

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C7×C13×Dic85 #44525860

order30940
automorphism?
homologyAbelianization (H1) = C4×C7×C13 · Schur multiplier (H2) = C1

Aliases

direct productC7×C13×Dic85

Splittings

derived, HallC5×C17 ⋊ C4×C7×C13
HallC5×C7×C13×C17 ⋊ C4
HallC7×C13×C17 ⋊ Dic5
HallC5×C13×C17 ⋊ C4×C7
HallC5×C7×C17 ⋊ C4×C13
HallC5×C7×C13 ⋊ Dic17
HallC13×C17 ⋊ C7×Dic5
HallC7×C17 ⋊ C13×Dic5
HallC5×C13 ⋊ C7×Dic17
HallC5×C7 ⋊ C13×Dic17
SylowC17 ⋊ C7×C13×Dic5
SylowC5 ⋊ C7×C13×Dic17

Subgroups

subgroupG/H
center, hypercenterC2×C7×C13D85
commutator, hypocenterC5×C17C4×C7×C13
FrattiniC2C7×C13×D85
Fitting, socle, prime radicalC2×C5×C7×C13×C17C2
cosocleC2×C5×C17C2×C7×C13
LCSG ▷ C5×C17
UCSC1 ◁ C2×C7×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 30940

Conjugacy classes & character table

8008 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30940, 10);