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C2×C19×#11717942 #44527529

order31122
automorphism?
homologyAbelianization (H1) = C2×C9×C19 · Schur multiplier (H2) = C1

Aliases

direct productC2×C19×#11717942

Splittings

derived, HallC7×C13 ⋊ C2×C9×C19
HallC2×C7×C13×C19 ⋊ C9
HallC7×C13×C19 ⋊ C2×C9
HallC2×C13×C19 ⋊ C7⋊C9
HallC2×C7×C19 ⋊ C13⋊C9
HallC13×C19 ⋊ C2×C7⋊C9
HallC2×C7×C13 ⋊ C9×C19
HallC7×C19 ⋊ C2×C13⋊C9
HallC2×C13 ⋊ C19×C7⋊C9
HallC2×C7 ⋊ C19×C13⋊C9
SylowC13 ⋊ C2×C19×C7⋊C9
SylowC7 ⋊ C2×C19×C13⋊C9

Subgroups

subgroupG/H
center, hypercenterC2×C3×C19#63271
commutator, hypocenterC7×C13C2×C9×C19
FrattiniC3C2×C19×#63271
Fitting, socle, prime radicalC2×C3×C7×C13×C19C3
cosocleC3×C7×C13C2×C3×C19
LCSG ▷ C7×C13
UCSC1 ◁ C2×C3×C19

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31122

Conjugacy classes & character table

3762 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31122, 12);