Finite Group Databasebeta

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D7×D1105 #44525948

order30940
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

direct productD7×D1105
unambiguous semidirect product(C5×D7)⋊D221
unambiguous semidirect product(C13×D7)⋊D85
unambiguous semidirect product(D7×C17)⋊D65

Splittings

Fitting, socle, derived, HallC5×C7×C13×C17 ⋊ C22
HallC7×C13×C17 ⋊ C2×D5
HallC5×C13×C17 ⋊ C2×D7
HallC5×C7×C17 ⋊ C2×D13
HallC5×C7×C13 ⋊ C2×D17
HallC13×C17 ⋊ D5×D7
HallC7×C17 ⋊ C2×D65
HallC7×C13 ⋊ C2×D85
HallC5×C17 ⋊ D7×D13
HallC5×C13 ⋊ D7×D17
HallC5×C7 ⋊ C2×D221
SylowC17 ⋊ D7×D65
SylowC13 ⋊ D7×D85
SylowC7 ⋊ C2×D1105
SylowC5 ⋊ D7×D221

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C7×C13×C17C22
LCSG ▷ C5×C7×C13×C17
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7735

Conjugacy classes & character table

2770 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30940, 98);