Finite Group Databasebeta

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D5×D1365 #41032014

order27300
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

direct productD5×D1365
unambiguous semidirect product(C3×D5)⋊D455
unambiguous semidirect product(C5×D5)⋊D273
unambiguous semidirect product(C7×D5)⋊D195
unambiguous semidirect product(D5×C13)⋊D105

Splittings

Fitting, socle, derived, HallC3×C52×C7×C13 ⋊ C22
HallC52×C7×C13 ⋊ C2×D3
HallC3×C52×C13 ⋊ C2×D7
HallC3×C52×C7 ⋊ C2×D13
HallC52×C13 ⋊ C2×D21
HallC3×C7×C13 ⋊ D52
HallC52×C7 ⋊ C2×D39
HallC7×C13 ⋊ D5×D15
HallC3×C52 ⋊ C2×D91
HallC3×C13 ⋊ D5×D35
SylowC52 ⋊ C2×D273
HallC3×C7 ⋊ D5×D65
SylowC13 ⋊ D5×D105
SylowC7 ⋊ D5×D195
SylowC3 ⋊ D5×D455

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C52×C7×C13C22
LCSG ▷ C3×C52×C7×C13
UCSC1

192 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 52 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) = 2730

Conjugacy classes & character table

2736 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 904);