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C5×C7×Dic5×ΓL(1,𝔽8) #28413141

order14700
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×Dic5×ΓL(1,𝔽8)
unambiguous semidirect product(C7×Dic5)⋊(C3×C5×C7)
unambiguous semidirect product(C5×C7×Dic5)⋊(C3×C7)

Splittings

derivedC5×C7 ⋊ C3×C4×C5×C7
HallC5×C72×Dic5 ⋊ C3
HallC52×C7×ΓL(1,𝔽8) ⋊ C4
HallC52×C72 ⋊ C3×C4
SylowC72 ⋊ C3×C5×Dic5
SylowC52 ⋊ C4×C7×ΓL(1,𝔽8)

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7D5×ΓL(1,𝔽8)
commutator, hypocenterC5×C7C3×C4×C5×C7
FrattiniC2C5×C7×D5×ΓL(1,𝔽8)
Fitting, socleC2×C52×C72C2×C3
prime radicalC2×C52×C7×ΓL(1,𝔽8)C2
cosocleC2×C5×C7C2×C3×C5×C7
LCSG ▷ C5×C7
UCSC1 ◁ C2×C5×C7

160 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Conjugacy classes & character table

1400 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14700, 320);