Finite Group Databasebeta

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C2×C7×#14519613 #41031841

order27300
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C7×#14519613

Splittings

Fitting, socleC2×C52×C7×C13 ⋊ C2×C3
derived, HallC52×C13 ⋊ C22×C3×C7
HallC2×C7×C5⋊D65 ⋊ C3
HallC7×C13×C52⋊C3 ⋊ C22
HallC52×C7×C13 ⋊ C22×C3
HallC2×C5⋊D65 ⋊ C3×C7
HallC13×C52⋊C3 ⋊ C22×C7
HallC7×C52⋊C3 ⋊ C2×D13
HallC52×C7 ⋊ C2×C3×D13
HallC7×C13 ⋊ C2×(C5⋊D5)⋊C3
HallC52⋊C3 ⋊ C2×C7×D13
SylowC52 ⋊ C2×C3×C7×D13
SylowC13 ⋊ C2×C7×(C5⋊D5)⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C7#14519613
commutator, cosocle, hypocenterC52×C13C22×C3×C7
FrattiniC1G
Fitting, socleC2×C52×C7×C13C2×C3
LCSG ▷ C52×C13
UCSC1 ◁ C2×C7

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2730

Conjugacy classes & character table

1064 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 731);