Finite Group Databasebeta

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D5×D1155 #37528679

order23100
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

direct productD5×D1155
unambiguous semidirect product(C3×D5)⋊D385
unambiguous semidirect product(C5×D5)⋊D231
unambiguous semidirect product(C7×D5)⋊D165
unambiguous semidirect product(D5×C11)⋊D105

Splittings

Fitting, socle, derived, HallC3×C52×C7×C11 ⋊ C22
HallC52×C7×C11 ⋊ C2×D3
HallC3×C52×C11 ⋊ C2×D7
HallC3×C52×C7 ⋊ C2×D11
HallC52×C11 ⋊ C2×D21
HallC3×C7×C11 ⋊ D52
HallC52×C7 ⋊ C2×D33
HallC7×C11 ⋊ D5×D15
HallC3×C52 ⋊ C2×D77
HallC3×C11 ⋊ D5×D35
SylowC52 ⋊ C2×D231
HallC3×C7 ⋊ D5×D55
SylowC11 ⋊ D5×D105
SylowC7 ⋊ D5×D165
SylowC3 ⋊ D5×D385

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C52×C7×C11C22
LCSG ▷ C3×C52×C7×C11
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) = 2310

Conjugacy classes & character table

2316 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 490);