Finite Group Databasebeta

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C2×C23×D79⋊C3 #36345520

order21804
automorphism?
homologyAbelianization (H1) = C22×C3×C23 · Schur multiplier (H2) = C2

Aliases

direct productC2×C23×D79⋊C3
unambiguous semidirect productD79⋊(C2×C3×C23)
unambiguous semidirect product(C79⋊C3)⋊(C22×C23)
unambiguous semidirect product(C2×D79)⋊(C3×C23)
unambiguous semidirect product(C2×C79⋊C3)⋊(C2×C23)
unambiguous semidirect product(C2×C23×D79)⋊C3

Splittings

Fitting, socleC2×C23×C79 ⋊ C2×C3
derived, SylowC79 ⋊ C22×C3×C23
HallC2×C23×D79 ⋊ C3
HallC23×C79⋊C3 ⋊ C22
HallC23×C79 ⋊ C22×C3
HallC2×D79 ⋊ C3×C23
HallC79⋊C3 ⋊ C22×C23

Subgroups

subgroupG/H
center, hypercenterC2×C23D79⋊C3
commutator, cosocle, hypocenterC79C22×C3×C23
FrattiniC1G
Fitting, socleC2×C23×C79C2×C3
LCSG ▷ C79
UCSC1 ◁ C2×C23

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3634

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21804, 15);