Finite Group Databasebeta

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C5×#19129706 #41031364

order27300
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#19129706

Splittings

derivedC5×C7×C13 ⋊ C3×C4×C5
HallC5×Dic455 ⋊ C3
HallC52×#63271 ⋊ C4
HallC52×C7×C13 ⋊ C3×C4
HallC52×C13 ⋊ ΓL(1,𝔽8)⋊C4
Hall#63271 ⋊ C5×Dic5
HallC52×C7 ⋊ Dic13⋊C3
HallC7×C13 ⋊ C3×C5×Dic5
SylowC52 ⋊ #11763964
SylowC13 ⋊ C5×ΓL(1,𝔽8)⋊Dic5
SylowC7 ⋊ C5×Dic65⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5C5⋊#10587723
commutator, hypocenterC5×C7×C13C3×C4×C5
FrattiniC2C5×C5⋊#10587723
Fitting, socleC2×C52×C7×C13C2×C3
prime radicalC2×C52×#63271C2
cosocleC2×C5×C7×C13C2×C3×C5
LCSG ▷ C5×C7×C13
UCSC1 ◁ C2×C5

128 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 44 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) = 1820

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 254);