Finite Group Databasebeta

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C2×C7×C3⋊D273 #37525683

order22932
automorphism?
homologyAbelianization (H1) = C22×C7 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C7×C3⋊D273
unambiguous semidirect product(C2×C3)⋊(C7×D273)
unambiguous semidirect product(C2×C7)⋊(C7×C3⋊D39)
unambiguous semidirect product(C2×C13)⋊(C7×C3⋊D21)

Splittings

Fitting, socleC2×C32×C72×C13 ⋊ C2
derivedC32×C7×C13 ⋊ C22×C7
HallC32×C72×C13 ⋊ C22
HallC72×C13 ⋊ C2×C3⋊D3
HallC32×C72 ⋊ C2×D13
HallC32×C13 ⋊ C2×C7×D7
SylowC72 ⋊ C2×C3⋊D39
SylowC13 ⋊ C2×C7×C3⋊D21
SylowC32 ⋊ C2×C7×D91

Subgroups

subgroupG/H
center, hypercenterC2×C7C3⋊D273
commutator, cosocle, hypocenterC32×C7×C13C22×C7
FrattiniC1G
Fitting, socleC2×C32×C72×C13C2
LCSG ▷ C32×C7×C13
UCSC1 ◁ C2×C7

312 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 102 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) = 3276

Conjugacy classes & character table

5754 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 1628);