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C109×Dic7⋊C9 #42117337

order27468
automorphism?
homologyAbelianization (H1) = C4×C9×C109 · Schur multiplier (H2) = C1

Aliases

direct productC109×Dic7⋊C9
unambiguous semidirect productDic7⋊(C9×C109)
unambiguous semidirect product(C7⋊C9)⋊(C4×C109)

Splittings

derived, SylowC7 ⋊ C4×C9×C109
HallC7⋊C9×C109 ⋊ C4
HallDic7×C109 ⋊ C9
HallC7×C109 ⋊ C4×C9
HallC7⋊C9 ⋊ C4×C109
HallDic7 ⋊ C9×C109

Subgroups

subgroupG/H
center, hypercenterC2×C3×C109AGL(1,𝔽7)
commutator, hypocenterC7C4×C9×C109
FrattiniC2×C3AGL(1,𝔽7)×C109
Fitting, socle, prime radicalC2×C3×C7×C109C2×C3
cosocleC2×C3×C7C2×C3×C109
LCSG ▷ C7
UCSC1 ◁ C2×C3×C109

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 27468

Conjugacy classes & character table

4578 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27468, 18);