Finite Group Databasebeta

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D7×C5⋊((C13⋊C3)⋊D7) #50304130

order38220
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productD7×C5⋊((C13⋊C3)⋊D7)
unambiguous semidirect product(D7×C13⋊C3)⋊D35

Splittings

Fitting, socle, derived, HallC5×C72×C13 ⋊ C22×C3
HallD7×D455 ⋊ C3
HallC5×C72×C13⋊C3 ⋊ C22
HallC72×C13⋊C3 ⋊ C2×D5
HallC72×C13 ⋊ C2×C3×D5
HallC5×C72 ⋊ C2×D13⋊C3
HallC5×C13⋊C3 ⋊ D72
HallC5×C13 ⋊ C3×D72
SylowC72 ⋊ C2×C5⋊(D13⋊C3)
HallC13⋊C3 ⋊ D7×D35
SylowC13 ⋊ C3×D7×D35
SylowC5 ⋊ D7×(C13⋊C3)⋊D7

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C72×C13C22×C3
LCSG ▷ C5×C72×C13
UCSC1

208 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 910

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 816);