D₇₅⋊D₉₁ #41031322

order	27300
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

D₇₅⋊D₉₁

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₃×C₇×C₁₃×C₂₅	C₂²
Frattini	C₅	D₁₅⋊D₉₁
socle	C₃×C₅×C₇×C₁₃	C₂×D₅
LCS	G ▷ C₃×C₇×C₁₃×C₂₅
UCS	C₁

120 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.

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

μ_t(G) = 6825

Polycyclic presentation:

2^2,3,5,7,13,5|d^5=g^4,d^a=d^4g,e^a=e^6,f^a=f^12,g^a=g^4,c^b=c^2,d^b=d^4g,g^b=g^4

1797 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 212);